Today I’ve discovered a new kind of product of funcoids which I call “simple product”.

It is defined by the formulas
$\left\langle \prod^{(S)}f \right\rangle x = \lambda i \in \mathrm{dom}\, f: \langle f_i \rangle x_i$ and $\left\langle \left( \prod^{(S)}f \right)^{-1} \right\rangle y = \lambda i \in \mathrm{dom}\, f:\langle f_i^{-1} \rangle y_i$.